Optimum Cross-Coupled Tracker for Pulse-Doppler Radar

Although there is a well-defined relation between range and range rate, in conventional pulse-Doppler tracking radars the range-gate and frequency control loops are usually closed independently. In this paper, the optimum cross- coupled stationary tracking filter is derived, in which the range error signal is used to boost the frequency loop, and vice versa. The filter is derived for a general case of target dynamics and uncorrelated white noise in both the range gate and frequency control channels. It is shown that its tracking performance is superior to that of the conventional uncoupled tracking loop for reliable frequency channel operation. In solving the usually difficult degenerated Riccati matrix equation, a simple solution is obtained by applying the method of completion of the square to matrixes.